Complicated non-linear relationship

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I came from an engineering background, so please excuse my ignorance in math.

Am looking for a mathematical interpretation for the following figure, here it is obvious that Z follows a non-linear behavior with x,y. if it is a one variable function we normally take its derivative and equate it to zero to find the maxims.

However, in this figure am dealing with a PDE and am clueless.

Please think of it as you are looking into mathematical problem and direct me where to look or what you think the pattern means, to be more exact, what does the marked points mean?

Thank you

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